Corner treatment for high-order local absorbing boundary conditions in high-frequency acoustic scattering

Axel Modave 1 Christophe Geuzaine 2 Xavier Antoine 3
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal computational domains for the finite element solution of high-frequency acoustic scattering problems. While high-order absorbing boundary conditions (HABCs) are accurate for smooth fictitious boundaries, the precision of the solution drops in the presence of corners if no specific treatment is applied. We present and analyze two strategies to preserve the accuracy of Padé-type HABCs at corners: first by using compatibility relations (derived for right angle corners) and second by regularizing the boundary at the corner. We show that the former strategy is well-adapted to right corners and efficient for nearly-right corners, while the later is better for very obtuse corners. Numerical results are proposed to analyze and compare the approaches for two-and three-dimensional problems.
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Submitted on : Friday, November 16, 2018 - 2:54:11 PM
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Axel Modave, Christophe Geuzaine, Xavier Antoine. Corner treatment for high-order local absorbing boundary conditions in high-frequency acoustic scattering. 2018. ⟨hal-01925160⟩

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